Abstract

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical random fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.

Received 11 December 2009Accepted 04 July 2010Published online 27 August 2010

Acknowledgments:

This paper was written under the support of the grant “Mathematical Modeling” of Växjö University and the grant QBIC of Tokyo University of Science (visiting fellowships March 2009 and March–April 2010). It was presented at “Feynman Festival,” June 2009. The author would like to thank Vladimir Manko for his critical comments which improved understanding of the model.